Understanding Graphs in Data Structures and Algorithms

Graphs are a fundamental concept in computer science, helping us model and solve problems involving connections and relationships. Whether it’s mapping out a social network, finding the shortest route between two cities, or representing a flow of information, graphs play a central role. At its core, a graph consists of two main components: **vertices** (or nodes) and **edges** (or arcs). Let’s dive into what graphs are, how they’re used, and why they’re so powerful in both theory and practice.

What is a Graph?

A graph is a collection of nodes (or vertices) connected by edges (or arcs). Each node represents an entity, while an edge represents a relationship or connection between two nodes. For example, in a social media network, each user is a vertex, and friendships or interactions are the edges that link them together.

There are different types of graphs depending on the nature of the connections between vertices:

1. Directed vs. Undirected Graphs:
- Directed Graph: In a directed graph, each edge has a direction, like one-way streets in a city. If there’s an edge from vertex A to vertex B, it doesn’t necessarily mean there’s an edge from B to A.
- Undirected Graph: In contrast, undirected graphs have bidirectional edges, like a two-way street. If there’s a connection between A and B, you can travel both ways.